Simulation of the Hurricane Dennis storm surge and considerations for vertical resolution

Abstract

A high-resolution storm surge model of Apalachee Bay in the northeastern Gulf of Mexico is developed using an unstructured grid finite-volume coastal ocean model (FVCOM). The model is applied to the case of Hurricane Dennis (July 2005). This storm caused underpredicted severe flooding of the Apalachee Bay coastal area and upriver inland communities. Accurate resolution of complicated geometry of the coastal region and waterways in the model reveals processes responsible for the unanticipated high storm tide in the area. Model results are validated with available observations of the storm tide. Model experiments suggest that during Dennis, excessive flooding in the coastal zone and the town of St. Marks, located up the St. Marks River, was caused by additive effects of coincident high tides (~10–15% of the total sea-level rise) and a propagating shelf wave (~30%) that added to the locally wind-generated surge. Wave setup, the biggest uncertainty, is estimated on the basis of empirical and analytical relations. The Dennis case is then used to test the sensitivity of the model solution to vertical discretization. A suite of model experiments is performed with varying numbers of vertical sigma (σ) levels, with different distribution of σ-levels within the water column and a varying bottom drag coefficient. The major finding is that the storm surge solution is more sensitive to resolution within the velocity shear zone at mid-depths compared to resolution of the upper and bottom layer or values of the bottom drag coefficient.

Appendix 1. Wave setup estimation

Setup at the shoreline is given by (Smith 2002):

$$ \bar{\eta }_{S} = \bar{\eta }_{\text{b}} + \left( {1 + {\frac{8}{{3\gamma_{\text{b}}^{2} }}}} \right)^{ - 1} H_{\text{b}} , $$

(5)

where $\bar{\eta }_{\text{b}}$ is setdown, $\gamma_{\text{b}}$ is the breaker depth index, and H _b is the wave height at incipient breaking. Setdown for regular waves can be estimated from (Longuet-Higgins and Stewart 1963):

$$ \bar{\eta }_{\text{b}} = - \frac{1}{8}{\frac{{H_{\text{b}}^{2} \kappa }}{{\sinh \left( {2\kappa d_{\text{b}} } \right)}}}, $$

(6)

where κ is the wavenumber and d _b is the water depth at breaking. The breaker depth index is

$$ \gamma_{\text{b}} = {\frac{{H_{\text{b}} }}{{d_{\text{b}} }}} . $$

(7)

Another important index that relates the wave height at incipient breaking and the wave height over the deep water, H ₀, is the breaker height index:

$$ \Upomega_{\text{b}} = {\frac{{H_{\text{b}} }}{{H_{0} }}} . $$

(8)

The breaker indices Eqs. 7 and 8 depend on beach slope, which can be estimated as an average bottom slope from the break point to one wavelength offshore (Smith 2002), and characteristics of the wave (Weggel 1972; Smith and Kraus 1991). Detailed surveys of the surf zone are necessary for measuring this parameter as the available bathymetric data are not of sufficiently fine resolution. Wang et al. (2006) measured the beach slope (β) at St. George Island to be 0.05–0.06, but it is expected to be <0.01 over mud and seagrass flats near the St. Marks River entrance and Shell Point. The following wave setup estimates are derived for the beach slope of 0.01.

For calculating wave setup, characteristics of the waves generated by a storm in deep water are required. Ideally, measurements of the wave height and period from buoys could be used for estimating the wave setup. Unfortunately, there are no wave measurements available over the northern WFS during Hurricane Dennis. Therefore, Young’s model (Young 1988) for fetch-limited waves is used to estimate the deep-water wave height (H ₀) and the spectral peak period of the wave (T₀):

$$ H_{0} = 0.0016{\frac{{w_{10}^{2} }}{g}}\left( {{\frac{gF}{{w_{10}^{2} }}}} \right)^{0.5} $$

(9)

$$ T_{0} = 0.045{\frac{{2\pi w_{10}^{{}} }}{g}}\left( {{\frac{gF}{{w_{10}^{2} }}}} \right)^{0.33} $$

(10)

where w ₁₀ is 10-m wind speed and F is wind fetch.

Wind fetch is estimated on the basis of the procedure outlined in Resio et al. (2002). Away from the coast, fetch is defined such that wind direction variations do not exceed 15 degrees and wind speed variations do not exceed 2.5 m s⁻¹ from the mean. If distance to the upwind coastline is smaller than the fetch, the coastline limits the fetch. Estimates of wind fetch (Fig. 14) have been obtained when the hurricane center is close to Apalachee Bay when the winds reach their local maximum over the Bay. There is uncertainty about what region should be considered for estimating deep-water wave characteristics. In this study, the following logic has been used to define the region (shown in Fig. 14) where deep-water waves traveling to Apalachee Bay are generated. One criterion is the region should be deeper than the half-length of the wind waves generated during the storm. Wind waves generated during a storm in this region are O(100 m); thus, the deep region is deeper than the 100-m isobath. Another criterion is that the waves should travel to Apalachee Bay. It is assumed that the peak wave direction matches the local wind direction. The maximum surge at the Apalachee Bay coast occurred between 19 and 21 UTC (Fig. 4), about 3–4 h after the time shown in Fig. 14. Over this time, a gravity wave can travel about 200–300 km (assuming the average depth to be 50 m). From the above discussion, a possible region of deep-water generation is identified (Fig. 14). Over this region, the wind field exhibits very low curvature of the wind streamlines, resulting in a long fetch in the range from 80 to 120 km with an average of 100 km.

Fig. 14

Wind fetch (km) estimated by the method of Resio et al. (2002). The wind field used for estimating the fetch is shown by the overlaid vectors. The location of NOAA NDBC station 42036 is shown. Anticipated region where deep-water waves that travel to the Apalachee Bay region are generated is marked by the white dashed box

Wind fields used in the model experiment reveal that the maximum sustained wind over the WFS during Hurricane Dennis was in the range 20–25 m s⁻¹ in agreement with FDEP (2006). The maximum sustained wind measured in this area (NOAA NDBC, buoy 42036, 28°30′0″N 84°31′0″W, location is shown in Fig. 14) was 23.5 m s⁻¹. Therefore, Eqs. 9 and 10 estimate that deep-water wave height in the studied region is in the range from 3.2 to 4.04 m and wave period is from 7.6 to 8.2-s.

Analytically derived estimates of the deep-water wave characteristics can be compared with simulated wave fields at 18:00 UTC 10 July 2005, (closest instant to the time shown in Fig. 14), from the regional North Atlantic Hurricane (NAH) NOAA WAVEWATCH III model (http://polar.ncep.noaa.gov/waves) shown in Fig. 15. The deep-water waves are considered to be the waves in the water at least 100 m depth. On the basis of the simulated significant wave direction, a possible region from where deep-water waves could travel to Apalachee Bay and contribute to the wave setup during the maximum storm surge (2–4 h later) is identified (marked by the white solid box in Fig. 15). Note that location of the area agrees with the earlier defined area for wind fetch. In this area, the significant height of the deep-water wave is 3.5–5 m with the period of 8–9-s. The analytical estimates of the deep-water wave height and period are close to the characteristics of the simulated waves. It is noteworthy that the region of maximum wave heights is not in the model domain. According to NAH simulation, on that date and time, waves greater than 10 m height with the period of 10-s were to the west of the Apalachicola Bay and did not contribute to the wave setup along the coast of Apalachee Bay.

Fig. 15

Significant wave height (left) and peak wave period (right) on July 10, 2005, at 18:00 UTC, from the regional NAH WaveWatch III wave prediction model of NOAA National Weather Service. Overlaid gray arrows are significant wave direction vectors. The dashed box roughly delineates the Apalachee Bay model domain. The solid box indicates anticipated region from where deep-water waves might have travelled to Apalachee Bay by the time of maximum storm surge

Wave length is derived from the approximate dispersion relation for the surface gravity wave (Eckart 1952):

$$ L_{0} \approx {\frac{{gT^{2} }}{2\pi }}\sqrt {\tanh \left( {\omega^{2} \frac{d}{g}} \right)} , $$

(11)

where ω is wave frequency and L ₀ is the length of the deep-water wave. The estimated deep-water wave length generated by Hurricane Dennis in Apalachee Bay is 90 m to 104 m.

The breaker height index is estimated as (Munk 1949):

$$ \Upomega_{\text{b}} = 0.3\left( {{\frac{{H_{0} }}{{L_{0} }}}} \right)^{{ - {1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}}} , $$

(12)

which, together with Eq. 8, gives the wave height at incipient breaking to be from 2.9 to 3.6 m. Following Weggel (1972), for regions with slopes less or equal than 0.1 and H ₀/L ₀ < 0.06, the breaker depth index is found as:

$$ \gamma_{\text{b}} = b - a{\frac{{H_{\text{b}} }}{{gT^{2} }}} $$

(13)

where a and b are empirically determined functions of the beach slope:

$$ \begin{aligned} a =\, & 43.8\left[ {1 - \exp \left( { - 19\beta } \right)} \right] \\ b = \,& 1.56\left[ {1 + \exp \left( { - 19.5\beta } \right)} \right]^{ - 1} \\ \end{aligned} $$

(14)

The breaker depth index is 0.81. With this, Eq. 7 provides the depth of breaking from 3.6 to 4.4 m. After substituting all required values into Eqs. 5 and 6, one gets the estimated setup from 0.44 to 0.54 m.